Detecting the periodicity of highly irregularly sampled light-curves with Gaussian processes: the case of SDSSJ025214.67-002813.7

Abstract: Based on a 20-year-long multiband observation of its light-curve, it was conjectured that the quasar SDSSJ025214.67-002813.7 has a periodicity of ~4.4 years. These observations were acquired at a highly irregular sampling rate and feature long intervals of missing data. In this setting, the inference over the light-curve's spectral content requires, in addition to classic Fourier methods, a proper model of the probability distribution of the missing observations. In this article, we address the detection of the periodicity of a light-curve from partial and irregularly-sampled observations using Gaussian processes, a Bayesian nonparametric model for time series. This methodology allows us to evaluate the veracity of the claimed periodicity of the abovementioned quasar and also to estimate its power spectral density. Our main contribution is the confirmation that considering periodic component definitely improves the modeling of the data, although being the source originally selected by a large sample of objects, the possibility that this is a chance result cannot be ruled out.